MinT - Best Known (234−126, 234, s)-Nets in Base 4

Best Known (234−126, 234, s)-Nets in Base 4

(234−126, 234, 130)-Net over F₄ — Constructive and digital

Digital (108, 234, 130)-net over F₄, using

t-expansion [i] based on digital (105, 234, 130)-net over F₄, using
- net from sequence [i] based on digital (105, 129)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 105 and N(F) ≥ 130, using
    - T₇ from the second tower of function fields by GarcÃa and Stichtenoth over F₄ [i]

(234−126, 234, 144)-Net over F₄ — Digital

Digital (108, 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]

(234−126, 234, 1344)-Net in Base 4 — Upper bound on s

There is no (108, 234, 1345)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 784 445859 810704 513896 253161 150674 695442 466133 026624 676157 019398 178932 654772 188796 180744 673470 412371 723291 466762 820671 400322 371322 403110 550080 > 4²³⁴ [i]