MinT - Best Known (235−135, 235, s)-Nets in Base 4

Best Known (235−135, 235, s)-Nets in Base 4

(235−135, 235, 104)-Net over F₄ — Constructive and digital

Digital (100, 235, 104)-net over F₄, using

t-expansion [i] based on digital (73, 235, 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]

(235−135, 235, 144)-Net over F₄ — Digital

Digital (100, 235, 144)-net over F₄, using

t-expansion [i] based on digital (91, 235, 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]

(235−135, 235, 1034)-Net in Base 4 — Upper bound on s

There is no (100, 235, 1035)-net in base 4, because

1 times m-reduction [i] would yield (100, 234, 1035)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 782 958617 975773 557885 717200 983181 756744 794954 033358 201699 508580 858451 247486 097086 389427 547218 862871 760509 546485 366896 273891 745509 356551 222720 > 4²³⁴ [i]