MinT - Best Known (258−168, 258, s)-Nets in Base 4

Best Known (258−168, 258, s)-Nets in Base 4

(258−168, 258, 104)-Net over F₄ — Constructive and digital

Digital (90, 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]

(258−168, 258, 129)-Net over F₄ — Digital

Digital (90, 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]

(258−168, 258, 688)-Net in Base 4 — Upper bound on s

There is no (90, 258, 689)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 230204 674196 900114 478850 921009 094354 828791 969629 570767 809109 014803 963937 428879 328843 923691 062290 728584 127378 854360 102678 493605 851256 095125 990094 796166 330480 > 4²⁵⁸ [i]