MinT - Best Known (102, 102+135, s)-Nets in Base 4

Best Known (102, 102+135, s)-Nets in Base 4

(102, 102+135, 104)-Net over F₄ — Constructive and digital

Digital (102, 237, 104)-net over F₄, using

t-expansion [i] based on digital (73, 237, 104)-net over F₄, using
- net from sequence [i] based on digital (73, 103)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 73 and N(F) ≥ 104, using
    - F₆ from the tower of function fields by GarcÃa and Stichtenoth over F₄ [i]

(102, 102+135, 144)-Net over F₄ — Digital

Digital (102, 237, 144)-net over F₄, using

t-expansion [i] based on digital (91, 237, 144)-net over F₄, using
- net from sequence [i] based on digital (91, 143)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 91 and N(F) ≥ 144, using
    - Drinfeld modules of rank 1 [i]

(102, 102+135, 1080)-Net in Base 4 — Upper bound on s

There is no (102, 237, 1081)-net in base 4, because

1 times m-reduction [i] would yield (102, 236, 1081)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 12541 254551 456876 964826 237859 033402 693029 498592 803471 710811 714350 179781 595992 686815 733853 670867 986753 044208 296873 723943 556112 520549 922606 165120 > 4²³⁶ [i]