MinT - Best Known (72, 72+166, s)-Nets in Base 4

Best Known (72, 72+166, s)-Nets in Base 4

(72, 72+166, 66)-Net over F₄ — Constructive and digital

Digital (72, 238, 66)-net over F₄, using

t-expansion [i] based on digital (49, 238, 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+166, 105)-Net over F₄ — Digital

Digital (72, 238, 105)-net over F₄, using

t-expansion [i] based on digital (70, 238, 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+166, 497)-Net in Base 4 — Upper bound on s

There is no (72, 238, 498)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 218667 755018 051948 623061 024708 640709 518102 991730 483245 417076 518397 330996 603400 610436 415840 468134 122763 994286 495175 647738 661672 375915 898408 921280 > 4²³⁸ [i]