MinT - Best Known (70, 70+134, s)-Nets in Base 4

Best Known (70, 70+134, s)-Nets in Base 4

(70, 70+134, 66)-Net over F₄ — Constructive and digital

Digital (70, 204, 66)-net over F₄, using

t-expansion [i] based on digital (49, 204, 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, 70+134, 105)-Net over F₄ — Digital

Digital (70, 204, 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, 70+134, 531)-Net in Base 4 — Upper bound on s

There is no (70, 204, 532)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 669 908987 880698 272573 345112 643777 295235 203149 080075 278435 785838 704631 820254 016981 346128 265697 524264 637831 094383 757505 519400 > 4²⁰⁴ [i]