MinT - Best Known (234−130, 234, s)-Nets in Base 4

Best Known (234−130, 234, s)-Nets in Base 4

(234−130, 234, 104)-Net over F₄ — Constructive and digital

Digital (104, 234, 104)-net over F₄, using

t-expansion [i] based on digital (73, 234, 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]

(234−130, 234, 144)-Net over F₄ — Digital

Digital (104, 234, 144)-net over F₄, using

t-expansion [i] based on digital (91, 234, 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]

(234−130, 234, 1174)-Net in Base 4 — Upper bound on s

There is no (104, 234, 1175)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 775 603767 539346 596930 297505 390770 587765 762722 928101 778496 864515 266878 296469 459748 722269 988931 681698 243044 655148 295142 144341 374665 227224 285940 > 4²³⁴ [i]