MinT - Best Known (76, 259, s)-Nets in Base 4

Best Known (76, 259, s)-Nets in Base 4

(76, 259, 104)-Net over F₄ — Constructive and digital

Digital (76, 259, 104)-net over F₄, using

t-expansion [i] based on digital (73, 259, 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]

(76, 259, 112)-Net over F₄ — Digital

Digital (76, 259, 112)-net over F₄, using

t-expansion [i] based on digital (73, 259, 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]

(76, 259, 516)-Net in Base 4 — Upper bound on s

There is no (76, 259, 517)-net in base 4, because

1 times m-reduction [i] would yield (76, 258, 517)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 229110 700028 739586 718257 502284 417379 806101 393565 438491 174879 913190 274809 929549 450865 553622 294727 639227 902197 708200 257531 054836 571090 191549 754633 992148 526336 > 4²⁵⁸ [i]