MinT - Best Known (62, 62+138, s)-Nets in Base 4

Best Known (62, 62+138, s)-Nets in Base 4

(62, 62+138, 66)-Net over F₄ — Constructive and digital

Digital (62, 200, 66)-net over F₄, using

t-expansion [i] based on digital (49, 200, 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]

(62, 62+138, 99)-Net over F₄ — Digital

Digital (62, 200, 99)-net over F₄, using

t-expansion [i] based on digital (61, 200, 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]

(62, 62+138, 437)-Net in Base 4 — Upper bound on s

There is no (62, 200, 438)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 2 962712 938324 605027 349406 912113 534942 195589 653919 181074 827806 773340 054224 866767 784823 244473 438033 272499 714894 073232 860250 > 4²⁰⁰ [i]