MinT - Best Known (181−93, 181, s)-Nets in Base 4

Best Known (181−93, 181, s)-Nets in Base 4

(181−93, 181, 104)-Net over F₄ — Constructive and digital

Digital (88, 181, 104)-net over F₄, using

t-expansion [i] based on digital (73, 181, 104)-net over F₄, using
- net from sequence [i] based on digital (73, 103)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 73 and N(F) ≥ 104, using
    - F₆ from the tower of function fields by GarcÃa and Stichtenoth over F₄ [i]

(181−93, 181, 129)-Net over F₄ — Digital

Digital (88, 181, 129)-net over F₄, using

t-expansion [i] based on digital (81, 181, 129)-net over F₄, using
- net from sequence [i] based on digital (81, 128)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 81 and N(F) ≥ 129, using
    - Drinfeld modules of rank 1 [i]

(181−93, 181, 1323)-Net in Base 4 — Upper bound on s

There is no (88, 181, 1324)-net in base 4, because

1 times m-reduction [i] would yield (88, 180, 1324)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 2 349037 464900 367737 134884 617975 006566 852711 796571 220014 703486 552369 600226 359036 479388 078490 538658 744900 342080 > 4¹⁸⁰ [i]