MinT - Best Known (200−81, 200, s)-Nets in Base 4

Best Known (200−81, 200, s)-Nets in Base 4

(200−81, 200, 130)-Net over F₄ — Constructive and digital

Digital (119, 200, 130)-net over F₄, using

t-expansion [i] based on digital (105, 200, 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]

(200−81, 200, 281)-Net over F₄ — Digital

Digital (119, 200, 281)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(200−81, 200, 5166)-Net in Base 4 — Upper bound on s

There is no (119, 200, 5167)-net in base 4, because

1 times m-reduction [i] would yield (119, 199, 5167)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 649407 689832 199195 710842 518386 519213 646870 739911 491245 354386 741488 669186 889501 537090 258525 967022 044605 637150 342478 985699 > 4¹⁹⁹ [i]