MinT - Best Known (230−113, 230, s)-Nets in Base 4

Best Known (230−113, 230, s)-Nets in Base 4

(230−113, 230, 130)-Net over F₄ — Constructive and digital

Digital (117, 230, 130)-net over F₄, using

t-expansion [i] based on digital (105, 230, 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]

(230−113, 230, 172)-Net over F₄ — Digital

Digital (117, 230, 172)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(230−113, 230, 2050)-Net in Base 4 — Upper bound on s

There is no (117, 230, 2051)-net in base 4, because

1 times m-reduction [i] would yield (117, 229, 2051)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 748016 502783 960726 140046 593769 784065 696802 922800 858507 132915 456548 213564 437086 231933 683111 902752 498677 731900 654814 849913 505355 034419 367168 > 4²²⁹ [i]