MinT - Best Known (217−123, 217, s)-Nets in Base 4

Best Known (217−123, 217, s)-Nets in Base 4

(217−123, 217, 104)-Net over F₄ — Constructive and digital

Digital (94, 217, 104)-net over F₄, using

t-expansion [i] based on digital (73, 217, 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]

(217−123, 217, 144)-Net over F₄ — Digital

Digital (94, 217, 144)-net over F₄, using

t-expansion [i] based on digital (91, 217, 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]

(217−123, 217, 1014)-Net in Base 4 — Upper bound on s

There is no (94, 217, 1015)-net in base 4, because

1 times m-reduction [i] would yield (94, 216, 1015)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 11309 330782 496298 946256 028495 740434 209138 658698 788405 398703 991524 365370 415768 147345 288808 084099 236338 866518 877500 335000 460977 533648 > 4²¹⁶ [i]