MinT - Best Known (242−120, 242, s)-Nets in Base 4

Best Known (242−120, 242, s)-Nets in Base 4

(242−120, 242, 130)-Net over F₄ — Constructive and digital

Digital (122, 242, 130)-net over F₄, using

t-expansion [i] based on digital (105, 242, 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]

(242−120, 242, 175)-Net over F₄ — Digital

Digital (122, 242, 175)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(242−120, 242, 2023)-Net in Base 4 — Upper bound on s

There is no (122, 242, 2024)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 50 551818 633020 972186 660566 491019 413898 681004 748647 723726 199698 778488 125375 862732 140619 699223 910938 382089 208644 179135 342697 312774 074380 075482 499096 > 4²⁴² [i]