MinT - Best Known (233−159, 233, s)-Nets in Base 4

Best Known (233−159, 233, s)-Nets in Base 4

(233−159, 233, 104)-Net over F₄ — Constructive and digital

Digital (74, 233, 104)-net over F₄, using

t-expansion [i] based on digital (73, 233, 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]

(233−159, 233, 112)-Net over F₄ — Digital

Digital (74, 233, 112)-net over F₄, using

t-expansion [i] based on digital (73, 233, 112)-net over F₄, using
- net from sequence [i] based on digital (73, 111)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 73 and N(F) ≥ 112, using
    - Drinfeld modules of rank 1 [i]

(233−159, 233, 527)-Net in Base 4 — Upper bound on s

There is no (74, 233, 528)-net in base 4, because

1 times m-reduction [i] would yield (74, 232, 528)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 47 918102 256938 919227 121705 396865 539638 547257 257371 860650 041904 991613 457343 556564 026016 685252 817700 013237 284621 146864 748225 530673 339024 438088 > 4²³² [i]