MinT - Best Known (72, 72+102, s)-Nets in Base 4

Best Known (72, 72+102, s)-Nets in Base 4

(72, 72+102, 66)-Net over F₄ — Constructive and digital

Digital (72, 174, 66)-net over F₄, using

t-expansion [i] based on digital (49, 174, 66)-net over F₄, using
- net from sequence [i] based on digital (49, 65)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 49 and N(F) ≥ 66, using
    - T₆ from the second tower of function fields by GarcÃa and Stichtenoth over F₄ [i]

(72, 72+102, 105)-Net over F₄ — Digital

Digital (72, 174, 105)-net over F₄, using

t-expansion [i] based on digital (70, 174, 105)-net over F₄, using
- net from sequence [i] based on digital (70, 104)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 70 and N(F) ≥ 105, using
    - Drinfeld modules of rank 1 [i]

(72, 72+102, 708)-Net in Base 4 — Upper bound on s

There is no (72, 174, 709)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 594 825192 533633 351848 409597 309381 616906 462237 326222 928889 808486 295104 038742 923501 866510 662823 599400 694480 > 4¹⁷⁴ [i]