MinT - Best Known (233−158, 233, s)-Nets in Base 4

Best Known (233−158, 233, s)-Nets in Base 4

(233−158, 233, 104)-Net over F₄ — Constructive and digital

Digital (75, 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]

(233−158, 233, 112)-Net over F₄ — Digital

Digital (75, 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]

(233−158, 233, 538)-Net in Base 4 — Upper bound on s

There is no (75, 233, 539)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 207 055664 552594 345954 738758 755380 543699 839019 088003 314639 385635 929709 530174 586282 636675 467430 664378 139856 579622 837456 501375 161233 557760 291072 > 4²³³ [i]