MinT - Best Known (258−164, 258, s)-Nets in Base 4

Best Known (258−164, 258, s)-Nets in Base 4

(258−164, 258, 104)-Net over F₄ — Constructive and digital

Digital (94, 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]

(258−164, 258, 144)-Net over F₄ — Digital

Digital (94, 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]

(258−164, 258, 753)-Net in Base 4 — Upper bound on s

There is no (94, 258, 754)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 234511 988736 345104 082263 439017 834904 680169 936624 500489 185171 924567 215067 571041 511806 878200 707701 481888 832748 720156 216536 787031 989175 707101 020986 823305 559240 > 4²⁵⁸ [i]