MinT - Best Known (243−119, 243, s)-Nets in Base 4

Best Known (243−119, 243, s)-Nets in Base 4

(243−119, 243, 130)-Net over F₄ — Constructive and digital

Digital (124, 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]

(243−119, 243, 182)-Net over F₄ — Digital

Digital (124, 243, 182)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(243−119, 243, 2193)-Net in Base 4 — Upper bound on s

There is no (124, 243, 2194)-net in base 4, because

1 times m-reduction [i] would yield (124, 242, 2194)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 49 967649 195157 315294 343401 377654 880562 710974 558366 802008 828196 636482 819508 495122 321753 309021 985910 421798 113789 549100 593928 897442 204829 042046 617536 > 4²⁴² [i]