MinT - Best Known (69, 69+106, s)-Nets in Base 4

Best Known (69, 69+106, s)-Nets in Base 4

(69, 69+106, 66)-Net over F₄ — Constructive and digital

Digital (69, 175, 66)-net over F₄, using

t-expansion [i] based on digital (49, 175, 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]

(69, 69+106, 99)-Net over F₄ — Digital

Digital (69, 175, 99)-net over F₄, using

t-expansion [i] based on digital (61, 175, 99)-net over F₄, using
- net from sequence [i] based on digital (61, 98)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 61 and N(F) ≥ 99, using
    - Drinfeld modules of rank 1 [i]

(69, 69+106, 625)-Net in Base 4 — Upper bound on s

There is no (69, 175, 626)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 2458 900371 895841 455804 462490 671487 190148 180356 687180 283748 464622 999524 552082 385799 630660 536960 302245 417264 > 4¹⁷⁵ [i]