MinT - Best Known (102−67, 102, s)-Nets in Base 4

Best Known (102−67, 102, s)-Nets in Base 4

(102−67, 102, 56)-Net over F₄ — Constructive and digital

Digital (35, 102, 56)-net over F₄, using

t-expansion [i] based on digital (33, 102, 56)-net over F₄, using
- net from sequence [i] based on digital (33, 55)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 33 and N(F) ≥ 56, using
    - F₅ from the tower of function fields by GarcÃa and Stichtenoth over F₄ [i]

(102−67, 102, 65)-Net over F₄ — Digital

Digital (35, 102, 65)-net over F₄, using

t-expansion [i] based on digital (33, 102, 65)-net over F₄, using
- net from sequence [i] based on digital (33, 64)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 33 and N(F) ≥ 65, using
    - Drinfeld modules of rank 1 [i]

(102−67, 102, 279)-Net in Base 4 — Upper bound on s

There is no (35, 102, 280)-net in base 4, because

1 times m-reduction [i] would yield (35, 101, 280)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 6 934023 886767 490496 333395 662829 422328 249224 538375 530130 420648 > 4¹⁰¹ [i]