MinT - Best Known (116, 116+127, s)-Nets in Base 4

Best Known (116, 116+127, s)-Nets in Base 4

(116, 116+127, 130)-Net over F₄ — Constructive and digital

Digital (116, 243, 130)-net over F₄, using

t-expansion [i] based on digital (105, 243, 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]

(116, 116+127, 168)-Net over F₄ — Digital

Digital (116, 243, 168)-net over F₄, using

t-expansion [i] based on digital (115, 243, 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]

(116, 116+127, 1612)-Net in Base 4 — Upper bound on s

There is no (116, 243, 1613)-net in base 4, because

1 times m-reduction [i] would yield (116, 242, 1613)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 50 172346 291172 081255 588949 868029 418901 692304 635480 884990 711671 408964 845497 464762 356436 505211 193912 039684 176927 973710 828460 741628 077081 028379 644480 > 4²⁴² [i]