MinT - Best Known (102−78, 102, s)-Nets in Base 32

Best Known (102−78, 102, s)-Nets in Base 32

(102−78, 102, 120)-Net over F₃₂ — Constructive and digital

Digital (24, 102, 120)-net over F₃₂, using

t-expansion [i] based on digital (11, 102, 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]

(102−78, 102, 177)-Net in Base 32 — Constructive

(24, 102, 177)-net in base 32, using

base change [i] based on digital (7, 85, 177)-net over F₆₄, using
- net from sequence [i] based on digital (7, 176)-sequence over F₆₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 7 and N(F) ≥ 177, using
    - a function field by GarcÃa and Quoos [i]

(102−78, 102, 225)-Net over F₃₂ — Digital

Digital (24, 102, 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]

(102−78, 102, 4271)-Net in Base 32 — Upper bound on s

There is no (24, 102, 4272)-net in base 32, because

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]