MinT - Best Known (157−88, 157, s)-Nets in Base 4

Best Known (157−88, 157, s)-Nets in Base 4

(157−88, 157, 66)-Net over F₄ — Constructive and digital

Digital (69, 157, 66)-net over F₄, using

t-expansion [i] based on digital (49, 157, 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]

(157−88, 157, 99)-Net over F₄ — Digital

Digital (69, 157, 99)-net over F₄, using

t-expansion [i] based on digital (61, 157, 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]

(157−88, 157, 773)-Net in Base 4 — Upper bound on s

There is no (69, 157, 774)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 34020 678374 176999 693382 807428 830495 495411 177882 976616 395317 499812 245514 727785 257592 377009 778016 > 4¹⁵⁷ [i]