MinT - Best Known (98−75, 98, s)-Nets in Base 32

Best Known (98−75, 98, s)-Nets in Base 32

(98−75, 98, 120)-Net over F₃₂ — Constructive and digital

Digital (23, 98, 120)-net over F₃₂, using

t-expansion [i] based on digital (11, 98, 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]

(98−75, 98, 128)-Net in Base 32 — Constructive

(23, 98, 128)-net in base 32, using

10 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]

(98−75, 98, 185)-Net over F₃₂ — Digital

Digital (23, 98, 185)-net over F₃₂, using

t-expansion [i] based on digital (21, 98, 185)-net over F₃₂, using
- net from sequence [i] based on digital (21, 184)-sequence over F₃₂, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 21 and N(F) ≥ 185, using
    - a curve from the manYPoints database [i]

(98−75, 98, 4154)-Net in Base 32 — Upper bound on s

There is no (23, 98, 4155)-net in base 32, because

1 times m-reduction [i] would yield (23, 97, 4155)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 100 637164 455677 812425 014628 227783 750396 991400 528991 560967 961008 484137 115956 492272 888834 507862 430389 829231 501647 813845 364201 757926 172238 789685 500772 > 32⁹⁷ [i]