MinT - Best Known (123, 256, s)-Nets in Base 4

Best Known (123, 256, s)-Nets in Base 4

(123, 256, 130)-Net over F₄ — Constructive and digital

Digital (123, 256, 130)-net over F₄, using

t-expansion [i] based on digital (105, 256, 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]

(123, 256, 168)-Net over F₄ — Digital

Digital (123, 256, 168)-net over F₄, using

t-expansion [i] based on digital (115, 256, 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]

(123, 256, 1741)-Net in Base 4 — Upper bound on s

There is no (123, 256, 1742)-net in base 4, because

1 times m-reduction [i] would yield (123, 255, 1742)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 3438 781611 645674 280399 639288 332315 508862 368568 849955 343882 969915 322306 381967 844243 589978 162869 216117 124717 264373 505962 227395 513250 135574 645871 494581 821274 > 4²⁵⁵ [i]