MinT - Best Known (118, 118+127, s)-Nets in Base 4

Best Known (118, 118+127, s)-Nets in Base 4

(118, 118+127, 130)-Net over F₄ — Constructive and digital

Digital (118, 245, 130)-net over F₄, using

t-expansion [i] based on digital (105, 245, 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]

(118, 118+127, 168)-Net over F₄ — Digital

Digital (118, 245, 168)-net over F₄, using

t-expansion [i] based on digital (115, 245, 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]

(118, 118+127, 1687)-Net in Base 4 — Upper bound on s

There is no (118, 245, 1688)-net in base 4, because

1 times m-reduction [i] would yield (118, 244, 1688)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 806 882699 272323 346759 278364 624281 771503 507588 198298 449407 966645 684539 873801 002798 687374 815153 733305 446193 949254 384172 845177 235156 499279 303618 502640 > 4²⁴⁴ [i]