MinT - Best Known (162−100, 162, s)-Nets in Base 4

Best Known (162−100, 162, s)-Nets in Base 4

(162−100, 162, 66)-Net over F₄ — Constructive and digital

Digital (62, 162, 66)-net over F₄, using

t-expansion [i] based on digital (49, 162, 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]

(162−100, 162, 99)-Net over F₄ — Digital

Digital (62, 162, 99)-net over F₄, using

t-expansion [i] based on digital (61, 162, 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]

(162−100, 162, 539)-Net in Base 4 — Upper bound on s

There is no (62, 162, 540)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 35 295615 844287 495838 167392 006564 053231 933812 589064 481685 860537 017729 517334 266301 424567 093053 886800 > 4¹⁶² [i]