MinT - Best Known (66, 66+126, s)-Nets in Base 4

Best Known (66, 66+126, s)-Nets in Base 4

(66, 66+126, 66)-Net over F₄ — Constructive and digital

Digital (66, 192, 66)-net over F₄, using

t-expansion [i] based on digital (49, 192, 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]

(66, 66+126, 99)-Net over F₄ — Digital

Digital (66, 192, 99)-net over F₄, using

t-expansion [i] based on digital (61, 192, 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]

(66, 66+126, 503)-Net in Base 4 — Upper bound on s

There is no (66, 192, 504)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 41 072417 681458 458023 249649 712268 488633 530015 714484 036166 763749 036316 778310 597722 918851 584498 194393 158525 102705 946312 > 4¹⁹² [i]