MinT - Best Known (82, 82+176, s)-Nets in Base 4

Best Known (82, 82+176, s)-Nets in Base 4

(82, 82+176, 104)-Net over F₄ — Constructive and digital

Digital (82, 258, 104)-net over F₄, using

t-expansion [i] based on digital (73, 258, 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]

(82, 82+176, 129)-Net over F₄ — Digital

Digital (82, 258, 129)-net over F₄, using

t-expansion [i] based on digital (81, 258, 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]

(82, 82+176, 581)-Net in Base 4 — Upper bound on s

There is no (82, 258, 582)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 232476 123054 534505 491596 506286 778790 572199 028432 420058 748563 418195 796029 233997 136485 855902 028411 809876 524508 382119 302208 428385 363893 327664 607745 165745 119680 > 4²⁵⁸ [i]