MinT - Best Known (234−137, 234, s)-Nets in Base 4

Best Known (234−137, 234, s)-Nets in Base 4

(234−137, 234, 104)-Net over F₄ — Constructive and digital

Digital (97, 234, 104)-net over F₄, using

t-expansion [i] based on digital (73, 234, 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]

(234−137, 234, 144)-Net over F₄ — Digital

Digital (97, 234, 144)-net over F₄, using

t-expansion [i] based on digital (91, 234, 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]

(234−137, 234, 952)-Net in Base 4 — Upper bound on s

There is no (97, 234, 953)-net in base 4, because

1 times m-reduction [i] would yield (97, 233, 953)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 192 874553 092549 107900 404511 668615 512765 291077 031985 470484 761094 491297 385744 812704 725931 045128 940703 591973 594519 556132 557581 927476 461787 867100 > 4²³³ [i]