MinT - Best Known (208−131, 208, s)-Nets in Base 4

Best Known (208−131, 208, s)-Nets in Base 4

(208−131, 208, 104)-Net over F₄ — Constructive and digital

Digital (77, 208, 104)-net over F₄, using

t-expansion [i] based on digital (73, 208, 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]

(208−131, 208, 112)-Net over F₄ — Digital

Digital (77, 208, 112)-net over F₄, using

t-expansion [i] based on digital (73, 208, 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]

(208−131, 208, 637)-Net in Base 4 — Upper bound on s

There is no (77, 208, 638)-net in base 4, because

1 times m-reduction [i] would yield (77, 207, 638)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 42391 596561 383368 329596 034559 412652 881102 642987 961298 409954 758188 732632 095323 021707 805676 716292 685409 597596 398364 450518 410985 > 4²⁰⁷ [i]