MinT - Best Known (231−137, 231, s)-Nets in Base 4

Best Known (231−137, 231, s)-Nets in Base 4

(231−137, 231, 104)-Net over F₄ — Constructive and digital

Digital (94, 231, 104)-net over F₄, using

t-expansion [i] based on digital (73, 231, 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]

(231−137, 231, 144)-Net over F₄ — Digital

Digital (94, 231, 144)-net over F₄, using

t-expansion [i] based on digital (91, 231, 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]

(231−137, 231, 893)-Net in Base 4 — Upper bound on s

There is no (94, 231, 894)-net in base 4, because

1 times m-reduction [i] would yield (94, 230, 894)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 3 176074 584284 579112 088169 524099 675465 345721 865710 837686 737638 682839 923193 864436 026398 271877 643368 359609 680361 110235 828576 361441 265915 104289 > 4²³⁰ [i]