MinT - Best Known (98, 258, s)-Nets in Base 4

Best Known (98, 258, s)-Nets in Base 4

(98, 258, 104)-Net over F₄ — Constructive and digital

Digital (98, 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]

(98, 258, 144)-Net over F₄ — Digital

Digital (98, 258, 144)-net over F₄, using

t-expansion [i] based on digital (91, 258, 144)-net over F₄, using
- net from sequence [i] based on digital (91, 143)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 91 and N(F) ≥ 144, using
    - Drinfeld modules of rank 1 [i]

(98, 258, 827)-Net in Base 4 — Upper bound on s

There is no (98, 258, 828)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 228238 965080 965779 946082 488783 756790 777121 433018 751922 047494 398049 002935 522707 757733 977108 756501 191921 772892 380060 871296 598813 995895 098977 303304 468813 738668 > 4²⁵⁸ [i]