MinT - Best Known (240−119, 240, s)-Nets in Base 4

Best Known (240−119, 240, s)-Nets in Base 4

(240−119, 240, 130)-Net over F₄ — Constructive and digital

Digital (121, 240, 130)-net over F₄, using

t-expansion [i] based on digital (105, 240, 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]

(240−119, 240, 173)-Net over F₄ — Digital

Digital (121, 240, 173)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(240−119, 240, 2041)-Net in Base 4 — Upper bound on s

There is no (121, 240, 2042)-net in base 4, because

1 times m-reduction [i] would yield (121, 239, 2042)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 793761 093103 571857 505790 261680 389891 242680 796814 160505 005784 410782 984703 059658 661746 678396 971465 947306 354102 411836 175502 685360 904429 854774 238160 > 4²³⁹ [i]