MinT - Best Known (70, 212, s)-Nets in Base 4

Best Known (70, 212, s)-Nets in Base 4

(70, 212, 66)-Net over F₄ — Constructive and digital

Digital (70, 212, 66)-net over F₄, using

t-expansion [i] based on digital (49, 212, 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]

(70, 212, 105)-Net over F₄ — Digital

Digital (70, 212, 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]

(70, 212, 513)-Net in Base 4 — Upper bound on s

There is no (70, 212, 514)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 43 558417 666989 728581 318399 318784 649715 342359 164427 018732 139483 515402 700028 170874 394617 439872 988275 777218 527893 403532 801219 433728 > 4²¹² [i]