MinT - Best Known (119, 119+131, s)-Nets in Base 4

Best Known (119, 119+131, s)-Nets in Base 4

(119, 119+131, 130)-Net over F₄ — Constructive and digital

Digital (119, 250, 130)-net over F₄, using

t-expansion [i] based on digital (105, 250, 130)-net over F₄, using
- net from sequence [i] based on digital (105, 129)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 105 and N(F) ≥ 130, using
    - T₇ from the second tower of function fields by GarcÃa and Stichtenoth over F₄ [i]

(119, 119+131, 168)-Net over F₄ — Digital

Digital (119, 250, 168)-net over F₄, using

t-expansion [i] based on digital (115, 250, 168)-net over F₄, using
- net from sequence [i] based on digital (115, 167)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 115 and N(F) ≥ 168, using
    - Drinfeld modules of rank 1 [i]

(119, 119+131, 1637)-Net in Base 4 — Upper bound on s

There is no (119, 250, 1638)-net in base 4, because

1 times m-reduction [i] would yield (119, 249, 1638)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 843984 940965 682598 347660 146898 581762 937610 563704 878554 880794 185603 822959 015984 523690 831049 001995 143774 096632 533739 522429 388096 275004 105812 208859 171285 > 4²⁴⁹ [i]