MinT - Best Known (120, 203, s)-Nets in Base 4

Best Known (120, 203, s)-Nets in Base 4

(120, 203, 130)-Net over F₄ — Constructive and digital

Digital (120, 203, 130)-net over F₄, using

t-expansion [i] based on digital (105, 203, 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]

(120, 203, 276)-Net over F₄ — Digital

Digital (120, 203, 276)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(120, 203, 4944)-Net in Base 4 — Upper bound on s

There is no (120, 203, 4945)-net in base 4, because

1 times m-reduction [i] would yield (120, 202, 4945)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 41 578289 054902 269273 354592 343195 151573 400876 033255 228245 171343 580394 343247 339283 845153 516585 507356 983330 344798 453627 638000 > 4²⁰² [i]