MinT - Best Known (24, 24+79, s)-Nets in Base 32

Best Known (24, 24+79, s)-Nets in Base 32

(24, 24+79, 120)-Net over F₃₂ — Constructive and digital

Digital (24, 103, 120)-net over F₃₂, using

t-expansion [i] based on digital (11, 103, 120)-net over F₃₂, using
- net from sequence [i] based on digital (11, 119)-sequence over F₃₂, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 11 and N(F) ≥ 120, using
    - a function field by SÃ©mirat [i]

(24, 24+79, 128)-Net in Base 32 — Constructive

(24, 103, 128)-net in base 32, using

t-expansion [i] based on (23, 103, 128)-net in base 32, using
- 5 times m-reduction [i] based on (23, 108, 128)-net in base 32, using
  - base change [i] based on digital (5, 90, 128)-net over F₆₄, using
    - net from sequence [i] based on digital (5, 127)-sequence over F₆₄, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 5 and N(F) ≥ 128, using
        a function field by SÃ©mirat [i]

(24, 24+79, 225)-Net over F₃₂ — Digital

Digital (24, 103, 225)-net over F₃₂, using

net from sequence [i] based on digital (24, 224)-sequence over F₃₂, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 24 and N(F) ≥ 225, using
  - a curve from the manYPoints database [i]

(24, 24+79, 4271)-Net in Base 32 — Upper bound on s

There is no (24, 103, 4272)-net in base 32, because

1 times m-reduction [i] would yield (24, 102, 4272)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 3374 328249 536198 776074 157134 972591 024709 782054 001907 526321 022105 703673 585722 093420 413829 288549 994262 789449 621895 560559 444761 112380 155477 358355 837654 370901 > 32¹⁰² [i]