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

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

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

Digital (119, 238, 130)-net over F₄, using

t-expansion [i] based on digital (105, 238, 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+119, 168)-Net over F₄ — Digital

Digital (119, 238, 168)-net over F₄, using

t-expansion [i] based on digital (115, 238, 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+119, 1945)-Net in Base 4 — Upper bound on s

There is no (119, 238, 1946)-net in base 4, because

1 times m-reduction [i] would yield (119, 237, 1946)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 49513 400679 929799 723618 596066 075070 078250 766151 297795 461243 523757 462662 890379 165119 113977 450513 686230 954484 833222 118603 570932 981029 878313 827968 > 4²³⁷ [i]