MinT - Best Known (233−129, 233, s)-Nets in Base 4

Best Known (233−129, 233, s)-Nets in Base 4

(233−129, 233, 104)-Net over F₄ — Constructive and digital

Digital (104, 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]

(233−129, 233, 144)-Net over F₄ — Digital

Digital (104, 233, 144)-net over F₄, using

t-expansion [i] based on digital (91, 233, 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]

(233−129, 233, 1199)-Net in Base 4 — Upper bound on s

There is no (104, 233, 1200)-net in base 4, because

1 times m-reduction [i] would yield (104, 232, 1200)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 47 755952 125094 192866 950993 577061 869419 540235 207830 426460 727709 858337 529061 712811 822250 795499 340537 092912 007479 069482 670411 106902 152413 906098 > 4²³² [i]