MinT - Best Known (99, 99+139, s)-Nets in Base 4

Best Known (99, 99+139, s)-Nets in Base 4

(99, 99+139, 104)-Net over F₄ — Constructive and digital

Digital (99, 238, 104)-net over F₄, using

t-expansion [i] based on digital (73, 238, 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]

(99, 99+139, 144)-Net over F₄ — Digital

Digital (99, 238, 144)-net over F₄, using

t-expansion [i] based on digital (91, 238, 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]

(99, 99+139, 978)-Net in Base 4 — Upper bound on s

There is no (99, 238, 979)-net in base 4, because

1 times m-reduction [i] would yield (99, 237, 979)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 51781 156308 410064 325295 756475 884091 481038 088323 539053 667217 664650 766603 605831 077265 536475 923706 761797 428359 666568 698386 795643 061516 644932 679176 > 4²³⁷ [i]