MinT - Best Known (235−139, 235, s)-Nets in Base 4

Best Known (235−139, 235, s)-Nets in Base 4

(235−139, 235, 104)-Net over F₄ — Constructive and digital

Digital (96, 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]

(235−139, 235, 144)-Net over F₄ — Digital

Digital (96, 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]

(235−139, 235, 917)-Net in Base 4 — Upper bound on s

There is no (96, 235, 918)-net in base 4, because

1 times m-reduction [i] would yield (96, 234, 918)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 778 709761 381797 759434 902544 358066 658491 626008 165954 510363 273254 343867 157112 389946 077903 637301 491797 286611 534802 468116 138676 161302 063563 889990 > 4²³⁴ [i]