MinT - Best Known (217−109, 217, s)-Nets in Base 4

Best Known (217−109, 217, s)-Nets in Base 4

(217−109, 217, 130)-Net over F₄ — Constructive and digital

Digital (108, 217, 130)-net over F₄, using

t-expansion [i] based on digital (105, 217, 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]

(217−109, 217, 152)-Net over F₄ — Digital

Digital (108, 217, 152)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(217−109, 217, 1745)-Net in Base 4 — Upper bound on s

There is no (108, 217, 1746)-net in base 4, because

1 times m-reduction [i] would yield (108, 216, 1746)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 11386 066665 224928 787464 251878 499146 315386 998357 270562 896724 349589 598882 561019 388153 751654 014608 399706 330923 204032 759724 230588 629536 > 4²¹⁶ [i]