MinT - Best Known (255−151, 255, s)-Nets in Base 4

Best Known (255−151, 255, s)-Nets in Base 4

(255−151, 255, 104)-Net over F₄ — Constructive and digital

Digital (104, 255, 104)-net over F₄, using

t-expansion [i] based on digital (73, 255, 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]

(255−151, 255, 144)-Net over F₄ — Digital

Digital (104, 255, 144)-net over F₄, using

t-expansion [i] based on digital (91, 255, 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]

(255−151, 255, 987)-Net in Base 4 — Upper bound on s

There is no (104, 255, 988)-net in base 4, because

1 times m-reduction [i] would yield (104, 254, 988)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 864 114082 560506 467078 641623 295769 797650 464979 392680 647276 174125 012986 523152 819796 569588 491029 189243 526108 635795 227301 628258 770015 625826 687463 718010 974191 > 4²⁵⁴ [i]