MinT - Best Known (238−164, 238, s)-Nets in Base 4

Best Known (238−164, 238, s)-Nets in Base 4

(238−164, 238, 104)-Net over F₄ — Constructive and digital

Digital (74, 238, 104)-net over F₄, using

t-expansion [i] based on digital (73, 238, 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]

(238−164, 238, 112)-Net over F₄ — Digital

Digital (74, 238, 112)-net over F₄, using

t-expansion [i] based on digital (73, 238, 112)-net over F₄, using
- net from sequence [i] based on digital (73, 111)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 73 and N(F) ≥ 112, using
    - Drinfeld modules of rank 1 [i]

(238−164, 238, 518)-Net in Base 4 — Upper bound on s

There is no (74, 238, 519)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 196216 082663 237739 796929 336141 550260 726292 880178 133343 854273 052205 992586 978705 206783 630566 853158 867639 001931 696219 695668 042198 175465 866370 114080 > 4²³⁸ [i]