MinT - Best Known (224−103, 224, s)-Nets in Base 4

Best Known (224−103, 224, s)-Nets in Base 4

(224−103, 224, 130)-Net over F₄ — Constructive and digital

Digital (121, 224, 130)-net over F₄, using

t-expansion [i] based on digital (105, 224, 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]

(224−103, 224, 207)-Net over F₄ — Digital

Digital (121, 224, 207)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(224−103, 224, 2797)-Net in Base 4 — Upper bound on s

There is no (121, 224, 2798)-net in base 4, because

1 times m-reduction [i] would yield (121, 223, 2798)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 181 942911 487397 192398 471079 738798 413481 459860 867911 784285 296625 013563 356618 219451 710319 247895 518007 109198 186515 734670 973363 079098 022200 > 4²²³ [i]