MinT - Best Known (197−48, 197, s)-Nets in Base 4

Best Known (197−48, 197, s)-Nets in Base 4

(197−48, 197, 1032)-Net over F₄ — Constructive and digital

Digital (149, 197, 1032)-net over F₄, using

4¹ times duplication [i] based on digital (148, 196, 1032)-net over F₄, using
- trace code for nets [i] based on digital (1, 49, 258)-net over F₂₅₆, using
  - net from sequence [i] based on digital (1, 257)-sequence over F₂₅₆, using
    - Niederreiter sequence [i]

(197−48, 197, 2067)-Net over F₄ — Digital

Digital (149, 197, 2067)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(197−48, 197, 285838)-Net in Base 4 — Upper bound on s

There is no (149, 197, 285839)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 40348 842086 679127 841664 607912 097859 740910 682160 284029 783188 226505 225817 324783 874858 243176 833945 435217 205913 121727 977464 > 4¹⁹⁷ [i]