MinT - Best Known (86, 86+98, s)-Nets in Base 4

Best Known (86, 86+98, s)-Nets in Base 4

(86, 86+98, 104)-Net over F₄ — Constructive and digital

Digital (86, 184, 104)-net over F₄, using

t-expansion [i] based on digital (73, 184, 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]

(86, 86+98, 129)-Net over F₄ — Digital

Digital (86, 184, 129)-net over F₄, using

t-expansion [i] based on digital (81, 184, 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]

(86, 86+98, 1121)-Net in Base 4 — Upper bound on s

There is no (86, 184, 1122)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 611 512350 900456 113317 474638 620440 623236 176845 503463 573221 149461 417013 474060 807465 741385 163094 854600 159163 809604 > 4¹⁸⁴ [i]