MinT - Best Known (235−125, 235, s)-Nets in Base 4

Best Known (235−125, 235, s)-Nets in Base 4

(235−125, 235, 130)-Net over F₄ — Constructive and digital

Digital (110, 235, 130)-net over F₄, using

t-expansion [i] based on digital (105, 235, 130)-net over F₄, using
- net from sequence [i] based on digital (105, 129)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 105 and N(F) ≥ 130, using
    - T₇ from the second tower of function fields by GarcÃa and Stichtenoth over F₄ [i]

(235−125, 235, 165)-Net over F₄ — Digital

Digital (110, 235, 165)-net over F₄, using

t-expansion [i] based on digital (109, 235, 165)-net over F₄, using
- net from sequence [i] based on digital (109, 164)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 109 and N(F) ≥ 165, using
    - Drinfeld modules of rank 1 [i]

(235−125, 235, 1442)-Net in Base 4 — Upper bound on s

There is no (110, 235, 1443)-net in base 4, because

1 times m-reduction [i] would yield (110, 234, 1443)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 766 488398 592777 903092 850273 266286 670117 381500 783130 717155 281337 343550 469670 452780 294685 886901 254065 009908 057615 227633 894514 188598 859669 746400 > 4²³⁴ [i]