MinT - Best Known (238−122, 238, s)-Nets in Base 4

Best Known (238−122, 238, s)-Nets in Base 4

(238−122, 238, 130)-Net over F₄ — Constructive and digital

Digital (116, 238, 130)-net over F₄, using

t-expansion [i] based on digital (105, 238, 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]

(238−122, 238, 168)-Net over F₄ — Digital

Digital (116, 238, 168)-net over F₄, using

t-expansion [i] based on digital (115, 238, 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]

(238−122, 238, 1704)-Net in Base 4 — Upper bound on s

There is no (116, 238, 1705)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 197981 713469 653480 481172 380462 998678 557726 309840 602178 659556 690245 874911 904015 462341 839008 927297 777275 537156 888226 646606 399944 054374 650112 738560 > 4²³⁸ [i]