MinT - Best Known (238−143, 238, s)-Nets in Base 4

Best Known (238−143, 238, s)-Nets in Base 4

(238−143, 238, 104)-Net over F₄ — Constructive and digital

Digital (95, 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]

(238−143, 238, 144)-Net over F₄ — Digital

Digital (95, 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]

(238−143, 238, 872)-Net in Base 4 — Upper bound on s

There is no (95, 238, 873)-net in base 4, because

1 times m-reduction [i] would yield (95, 237, 873)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 52260 768030 431989 683295 854588 649909 845038 424128 919799 587320 049289 870495 107510 675485 181145 903792 312810 549944 410282 928645 875217 046598 476058 631640 > 4²³⁷ [i]