MinT - Best Known (238−162, 238, s)-Nets in Base 4

Best Known (238−162, 238, s)-Nets in Base 4

(238−162, 238, 104)-Net over F₄ — Constructive and digital

Digital (76, 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]

(238−162, 238, 112)-Net over F₄ — Digital

Digital (76, 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]

(238−162, 238, 542)-Net in Base 4 — Upper bound on s

There is no (76, 238, 543)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 219402 050616 590864 449473 042444 925552 582454 715171 319726 620865 687684 107984 529066 556297 843088 382303 709103 183878 485424 495930 867284 895454 910499 653360 > 4²³⁸ [i]