MinT - Best Known (99, 99+155, s)-Nets in Base 4

Best Known (99, 99+155, s)-Nets in Base 4

(99, 99+155, 104)-Net over F₄ — Constructive and digital

Digital (99, 254, 104)-net over F₄, using

t-expansion [i] based on digital (73, 254, 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+155, 144)-Net over F₄ — Digital

Digital (99, 254, 144)-net over F₄, using

t-expansion [i] based on digital (91, 254, 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+155, 872)-Net in Base 4 — Upper bound on s

There is no (99, 254, 873)-net in base 4, because

1 times m-reduction [i] would yield (99, 253, 873)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 214 494321 419345 236653 209750 266282 345395 174215 678877 918491 169841 095236 223053 741522 060316 101386 055313 574906 110724 257244 659743 334832 549139 622402 397439 579968 > 4²⁵³ [i]