MinT - Best Known (97, 240, s)-Nets in Base 4

Best Known (97, 240, s)-Nets in Base 4

(97, 240, 104)-Net over F₄ — Constructive and digital

Digital (97, 240, 104)-net over F₄, using

t-expansion [i] based on digital (73, 240, 104)-net over F₄, using
- net from sequence [i] based on digital (73, 103)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 73 and N(F) ≥ 104, using
    - F₆ from the tower of function fields by GarcÃa and Stichtenoth over F₄ [i]

(97, 240, 144)-Net over F₄ — Digital

Digital (97, 240, 144)-net over F₄, using

t-expansion [i] based on digital (91, 240, 144)-net over F₄, using
- net from sequence [i] based on digital (91, 143)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 91 and N(F) ≥ 144, using
    - Drinfeld modules of rank 1 [i]

(97, 240, 909)-Net in Base 4 — Upper bound on s

There is no (97, 240, 910)-net in base 4, because

1 times m-reduction [i] would yield (97, 239, 910)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 836379 394666 037271 479794 413887 877879 300322 904019 844501 395305 120671 125335 047658 802178 204481 177961 750923 109747 332025 933330 527158 900384 783359 160600 > 4²³⁹ [i]