MinT - Best Known (254−159, 254, s)-Nets in Base 4

Best Known (254−159, 254, s)-Nets in Base 4

(254−159, 254, 104)-Net over F₄ — Constructive and digital

Digital (95, 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]

(254−159, 254, 144)-Net over F₄ — Digital

Digital (95, 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]

(254−159, 254, 790)-Net in Base 4 — Upper bound on s

There is no (95, 254, 791)-net in base 4, because

1 times m-reduction [i] would yield (95, 253, 791)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 221 945907 059006 398652 549834 989419 799499 357971 199633 513220 902466 744830 784241 320843 451670 523541 384281 040421 973518 271888 598118 755158 767364 098491 293924 352288 > 4²⁵³ [i]